# 3 Density

Provided by Kenan Fellows Program.

Students will determine the density of two unknown liquids by collecting mass and volume data. Each group of students will be given a different volume of the liquids to measure; they will combine their data to create a graph. Using the graph students will determine the density of the two liquids by calculating the slope of the two lines. Students will also use a graphing calculator to determine the slope of the two lines.

This activity is a wonderful way to integrate Chemistry and Algebra II because the measuring of density is simple enough to do in an Algebra II class and using a hand-drawn graph and a calculator to determine the slope are skills students need to master for Algebra II. It also shows students a use for slope in a data collection scenario.

## Learning outcomes

Students will:

- Accurately measure the volume and mass of a liquid
- Graph the class data by hand and determine the slope of the lines
- Graph the class data using a graphing calculator and determine the slope of the lines
- Identify the slope of the lines as the density of the liquids
- Identify the liquids from their respective densities

## Teacher planning

### Time required

50 minutes

### Materials needed

- 2 liquids
- balances
- 10 ml and 25 ml graduated cylinders
- graphing calculators
- graph paper
- reference tables with densities of liquids

### Student handouts

- Density lab
- Document by the author
- Open as PDF (85 KB, 3 pages; also available as Microsoft Word document)

## Pre-activities

The teacher should make sure that students can calculate density. They must also be able to calculate the slope of a line and use a graphing calculator to input data and graph it. Teach or review how to calculate percent error.

## Activities

- Begin the lesson by demonstrating how to calculate the density of a liquid.
- Also explain how to accurately measure mass and volume of a liquid.
- Review how to determine the slope of a line from a graph and on the calculator.
- Begin the lab with a discussion. Explain to students that the density of a substance can be determined by obtaining the mass of a specific volume of that substance. This provides a value of density based on one trial or one set of experimental data. A more accurate density can be obtained by multiple trials. Then the data can be graphed. The slope of the graph will provide a more accurate value of density.
Tell students that each lab team will obtain one set of data, both mass and volume, for one of two liquids. Then the class data will be pooled so that a graph of each liquid can be prepared. Since the final results depend on each lab team, you must be very careful in all measurements.

Remind students that the mass of the liquid depends on the amount or volume of the sample. Therefore the volume is the independent variable in this experiment. The mass is the dependent variable. The slope of a graph is best determined by selecting points that are further apart on the graph. Slope (

*m*) equals a change in*y*divided by a change in*x*or m = Δy/Δx.Explain that the calculator provides a quick way to determine the slope of a graph. The class will determine the slope of the data for Liquid A and B during this lab. Experimental data is never perfect. Therefore, the lines will not be perfectly straight. The calculator can be used to determine the best-fit line and allow you to more clearly see the points that are not on the slope.

Wrap up the discussion by emphasizing that every pure substance has its own unique value of density. Density is considered to be an intensive property, and can be used to identify a substance.

- Ask students to complete the pre-lab questions on the lab sheet. Before beginning the lab, go over the questions as a class to ensure everyone has the correct responses. Students will be answering the following questions:
- In what units should density be recorded in this lab?
- For correct graphing, on what axis should the independent variable be placed?
- What specific variable will be graphed on the x-axis in this lab?
- What specific variable will be graphed on the y-axis in this lab?
- How is the slope of a line calculated?
- Which gives more accurate results: one trial or repeated trials of lab measurement?

- Have students collect and accurately record mass and volume data for the two liquids.
- Students should write their data on the board or overhead for all to copy.
- Once all data is collected the students should complete the post-lab questions.
- The teacher should use the class data to determine the slope of the two lines of data provided by the students for checking their answers later.

## Assessment

Check the answers to the post-lab questions.

## Critical vocabulary

- density
- a measure of how much mass is contained in a given unit volume (density = mass/volume)
- slope
- the rate at which an ordinate of a point of a line on a coordinate plane changes with respect to a change in the abscissa; the tangent of the angle of inclination of a line, or the slope of the tangent line for a curve or surface
- line of best fit
- a straight line used as a best approximation of a summary of all the points in a scatter-plot
The position and slope of the line are determined by the amount of correlation between the two, paired variables involved in generating the scatter-plot. This line can be used to make predictions about the value of one of the paired variables if only the other value in the pair is known.

- mass
- a property of matter equal to the measure of an object’s resistance to changes in either the speed or direction of its motion
The mass of an object is not dependent on gravity and therefore is different from but proportional to its weight.

- volume
- the magnitude of the three-dimensional space enclosed within or occupied by an object, geometric solid, etc.
- linear regression
- the relation between variables when the regression equation is linear, e.g., y = ax + b
- list
- a series of numbers
- stat plot
- a feature on the graphing calculator used to plot statistical data stored in lists
- percent error
- the percent of difference between two values is the ratio of their absolute difference to the magnitude of the accepted value, expressed as a percent
It quantifies the accuracy of a measurement.

(measured value - actual value)/actual value × 100%

## Comments

This activity works best with collaboration between science and math teachers, although both can do it separately.

- Common Core State Standards
- English Language Arts (2010)
#### Science & Technical Subjects

- Grades 11-12
- 11-12.LS.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.

- Grades 9-10
- 9-10.LS.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

- Grades 11-12
- Mathematics (2010)
#### Grade 8

- Functions
- 8.F.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph....

- Functions
#### High School: Functions

- Linear, Quadratic, & Exponential Models
- FUN.LQE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

- Linear, Quadratic, & Exponential Models
#### High School: Statistics & Probability

- Interpreting Categorical & Quantitative Data
- SP.ICQ.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function...

- Interpreting Categorical & Quantitative Data

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 9–12 — Algebra 2

**Goal 2**: Algebra - The learner will use relations and functions to solve problems.**Objective 2.04**: Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.- Interpret the constants, coefficients, and bases in the context of the data.
- Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

### Science (2005)

#### Grade 9–12 — Chemistry

**Goal 1**: The learner will develop abilities necessary to do and understand scientific inquiry.**Objective 1.01**: Design, conduct and analyze investigations to answer questions related to chemistry.- Identify questions and suggest hypotheses.
- Identify variables.
- Use a control when appropriate.
- Select and use appropriate measurement tools.
- Collect and organize data in tables, charts and graphs.
- Analyze and interpret data.
- Explain observations.
- Make inferences and predictions.
- Explain the relationship between evidence and explanation.
- Identify how scientists share findings.

**Objective 1.03**: Analyze experimental designs with regard to safety and use safe procedures in laboratory investigations:- Identify and avoid potential safety hazards given a scenario.
- Differentiate between safe and unsafe procedures.
- Use information from the MSDS (Material Safety Data Sheets) to assess chemical hazards.

**Goal 2**: The learner will build an understanding of the structure and properties of matter.**Objective 2.04**: Identify substances using their physical properties:- Melting points.
- Boiling points.
- Density.
- Solubility.